42 ideas
| 15957 | Essential definitions show the differences that discriminate things, and make them what they are [Boyle] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 15965 | Boyle attacked a contemporary belief that powers were occult things [Boyle, by Alexander,P] |
| 16735 | In the 17th century, 'disposition' usually just means the spatial arrangement of parts [Boyle, by Pasnau] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 16034 | Form is not a separate substance, but just the manner, modification or 'stamp' of matter [Boyle] |
| 15953 | To cite a substantial form tells us what produced the effect, but not how it did it [Boyle] |
| 15962 | Boyle's term 'texture' is not something you feel, but is unobservable structures of particles [Boyle, by Alexander,P] |
| 15964 | Boyle's secondary qualities are not illusory, or 'in the mind' [Boyle, by Alexander,P] |
| 16736 | Explanation is generally to deduce it from something better known, which comes in degrees [Boyle] |
| 15960 | Explanation is deducing a phenomenon from some nature better known to us [Boyle] |
| 16737 | The best explanations get down to primary basics, but others go less deep [Boyle] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 15952 | The corpuscles just have shape, size and motion, which explains things without 'sympathies' or 'forces' [Boyle, by Alexander,P] |
| 15972 | The corpuscular theory allows motion, but does not include forces between the particles [Boyle, by Alexander,P] |
| 15961 | I don't see how mere moving matter can lead to the bodies of men and animals, and especially their seeds [Boyle] |